In a rational world, Republicans would get the blame for the budget mess in Washington. In the George W. Bush era, they frittered impressive surpluses into unprecedented deficits. In 2011 they threatened to force the U.S. government into default if President Obama didn’t accept massive spending cuts, essentially taking the global economy hostage; the current sequester was part of their ransom. And now, even though the deficit is shrinking, even though just about everyone agrees that the sequester’s haphazard cuts will damage a fragile economy, GOP leaders won’t even discuss an alternative that includes new tax revenue.

Unfortunately, we don’t live in a rational world. The Beltway establishment recognizes the intransigence of the GOP, but the capital’s scorekeepers are incapable of blaming just one side. Their solution to the stalemate is just like Obama’s: a mix of spending cuts and tax hikes. But they still can’t resist pox-on-both-houses narratives. Why won’t Obama lead?

The answer is that the president isn’t omnipotent; he can’t bend the opposition to his will through schmoozing or fortitude. And Obama has already compromised, agreeing to $1.5 trillion in spending cuts and even proposing modest entitlement reforms. The only way Obama could fulfill the punditocracy’s dreams of bipartisan agreement would be to drop his demand for new revenues and cave to the tax-phobic Republicans he thumped in November.

So he should cave — not to appease the chattering classes, unify Washington or show the country he’s open to compromise. He should cave to ease pain, advance his agenda and improve the country in tangible ways.

Forget the dopey spats over White House tours and Easter-egg rolls. The sequester will cause real harm, so the President ought to at least try to replace it. And the pursuit of new revenue, while a reasonable goal, is not as important as his other goals — like avoiding short-term austerity that could derail the recovery, promoting long-term prosperity through targeted investments and tax reform, moving the budget in a fairer direction and preventing the GOP from taking more hostages in the future. He can’t possibly get a deal with everything he wants. But Republicans are so eager to avoid new taxes — and to make Obama look weak — that he might get a lot of what he wants if he gives them their top priority.

For example, everyone knows that the tax code is riddled with inefficient and indefensible loopholes and giveaways, from small perks for corporate-jet owners to the carried-interest outrage that helps Mitt Romney pay a lower rate than you do. Republicans say they’re willing to ditch some of those goodies but only if the proceeds are used to lower rates. Fine! Obama can insist on lowering middle-class rates, which would boost the economy and enable him to keep his long-standing promises to give ordinary Americans a permanent tax break. He provided temporary relief to the nonrich throughout his first term, but it expired with the fiscal cliff in January. This might be his best, last chance to make the tax code more rational and more progressive.

On spending, Republicans have already signaled that they want more cuts but that they don’t care too much about what gets cut. They’ve even offered Obama some flexibility to make the cuts, hoping he’ll be blamed for unpopular ones. Fine! Obama can whack programs that don’t promote his priorities, like fossil-fuel subsidies and sprawl roads; he can also demand back-loaded cuts that won’t kill jobs now. And he can protect the “win the future” stuff he cares about, like research and clean energy, as well as the safety net that Paul Ryan’s budget aims to shred.

Ultimately, Republicans might say no. They seem O.K. with the sequester, their base hates deals with Obama, and a stagnant economy could help them in 2014. So maybe there’s no deal. But Obama has spent the past four years pursuing change that’s possible, not change that’s perfect. He’s usually tried to do what he’s said he would — on energy, health care, education, taxation — but he’s also emphasized deeds over words. If he’s willing to surrender his demand for new taxes, he might be able to improve the status quo.

Perhaps it seems unfair that a newly re-elected President should have to settle for half a loaf, especially when he has to accommodate such unreasonable opponents. But they were re-elected too. So if Obama wants to keep making change, he’ll need to keep working in their crazy world.

This article is featured in the Commentary section in the April 1 issue of TIME Magazine